Problem 5 In order to test whether a box of 80 lemonades meets qualification, a manufacturer picks 20 items at random. If none are defective, the box is accepted. If at least one is defective, the manufacturer - who turns out to be quite unscrupulous - mixes the 20 lemonades back into the 80, then again picks 20 at random. This time, if none are defective, the box is accepted; if at least one is defective, then the manufacturer finally rejects the box. If a box of 80 lemonades has 5 defective lemonades, what is the probability that it gets accepted?

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